With the progress of the Internet, in particular, because of the expectation for progress in cloud computing, an increase in capability of Ethernet-based communication is an urgent challenge. As the next-generation high-speed 40 G/100 G Ethernet (registered trademark) standard, IEEE 802.3ba (NPL 1) was released in 2010, and discussions have been made. In particular, the range of several tens m to several tens km in transmission distance corresponds to a distance necessary for connection in a data center or between data centers, and is focused on because of large potential demand. In this standard, in the range exceeding several tens m, the use of optical communication is recommended because the attenuation of an electric signal is large, and also in consideration of economic efficiency, a multi-lane transmission system capable of avoiding the heavy use of high-speed LSIs (Large Scale Integration) is recommended. In particular, for a transmission distance of several hundreds m or more, a wavelength division multiplexing system using four wavelengths in the wavelength arrangement such as LAN-WDM (Local Area Network Wavelength Division Multiplexing) or CWDM (Coarse Wavelength Division Multiplexing) in the 1.3 μm band is recommended.
Devices responsible for realizing such transmission systems closest to physical media are optical transceivers. In general, an optical transceiver is configured to include: a connector part that inputs/outputs optical and electrical signals; a TOSA (Transmitter Optical Sub-Assembly) and ROSA (Receiver Optical Sub-Assembly) that perform photoelectric conversion; an electronic circuit that controls and monitors respective parts; and an electronic circuit that performs signal conversion as necessary. Further, the ROSA used for such transmission systems is assembled with: an optical filter that demultiplexes a multi-lane signal including four waves in the 1.3 μm band; four PDs (Photo Diodes); a TIA (Trans-Impedance Amplifier) close to the PDs; and the like. For example, there has been reported a ROSA that is prepared using an optical module assembled with four small TFFs (Thin Film Filters) and a total reflection mirror as a 4-ch optical demultiplexing filter (see NPL 2). The ROSA reported in this literature realizes an extremely small module size as a result of using the small TFF chips and advanced packaging technology. However, the optical module prepared using the plurality of TFFs becomes more difficult to manufacture with increasing the number of channels and reducing the size, and a reduction in size and a reduction in cost cannot be easily achieved at the same time.
On the other hand, an arrayed waveguide grating (AWG) optical filter prepared with a silica-based PLC (Planar Lightwave Circuit), which is a multi-channel optical filter, is widely used for telecommunication transmission equipment because of the excellence not only in wavelength demultiplexing characteristics but in mass productivity and reliability. Further, the AWG optical filter is characterized by excellent economic efficiency and mass productivity because in particular, in the case where the number of channels is large or a reduction in size is required, as compares with the optical filter having arranged TFFs, the number of manufacturing steps is small, and the required tolerance of mechanical precision (TFF arrangement precision and waveguide exposure precision) is large.
However, the AWG had a problem once. In the initial stage of AWG development, there was a problem that designing an AWG having a channel spacing of several 10 nm or more caused an increase in chip size. However, such a restriction has been significantly relaxed by devising an arrayed waveguide arrangement, and therefore today, even an AWG having a channel spacing of 100 nm or more can be easily realized (see PTLs 1 and 2).
Regarding an AWG design method, a first conventional example is described first using FIG. 1. FIG. 1 illustrates the outline of a conventional arrayed waveguide grating optical filter. As illustrated in FIG. 1, the arrayed waveguide grating optical filter is configured to include slab waveguides 1 and 2, arrayed waveguide group 3, input waveguide 4, and output waveguides 5. Note that to appropriately operate the arrayed waveguide grating optical filter, it is necessary that connecting points between the waveguide group, which connects the slab waveguides 1 and 2 to each other, and the slab waveguides 1 and 2 are present on extended lines of straight lines radially drawn from focal points of the slab waveguides 1 and 2 on the input and output waveguide sides, and between mutually adjacent ones of all waveguides, the length is different by a certain amount (d0), and monotonically increases or decreases.
In the arrayed waveguide grating filter illustrated in FIG. 1, the arrayed waveguide group 3 is configured by sequentially connecting respective waveguides, i.e., linear waveguides 3a, arcuate waveguides 3c, and linear waveguides 3b, respectively. Note that in the first conventional example, protruding directions of arcs of the arcuate waveguides 3c are only one direction, i.e., in the case of FIG. 1, an upward direction, and therefore relative to lower waveguides of the arrayed waveguide group 3, upper waveguides are longer. However, by appropriately select lengths of the linear waveguides 3a and 3b and radii of the arcuate waveguides 3c, the array waveguide group 3 can be arranged such that between any adjacent ones of all the waveguides, the length is different by the certain amount (d0).
On the other hand, the difference (d0) in length between any adjacent waveguides of the array waveguide group 3 has a relationship given by the following expression (1) with respective parameters (λ0: center wavelength, ng: group refractive index, and FSR: free spectral range) of the arrayed waveguide grating optical filter. Note that in the following, d0 is referred to as a waveguide length difference, and d0×ne, which is d0 multiplied by an effective refractive index ne, is referred to as an optical path length difference.Wavelength interval×Maximum number of channels<λ02/(d0×ng)=FSR  (1)
In the case where a required wavelength interval is large, or a large number of channels are required, it is necessary to set the waveguide length difference d0 smaller; however, in the case where the waveguide length difference d0 is extremely small, in the arrayed waveguide group 3, an upper waveguide and a lower waveguide come into contact with or intersect with each other to make it difficult to appropriately operate the arrayed waveguide grating optical filter. That is, according to the first conventional technique described above, from geometrical constraints, a settable waveguide length difference has a lower limit, and therefore the design method according to the first conventional example makes it geometrically impossible to set the optical path length difference extremely short, or even if the setting is possible, may anomalously increase the size of a circuit.
In the case of attempting to realize such a device as a waveguide type, the size of a usable substrate material has a certain limit, and accordingly in the case where the size of a circuit exceeds the certain limit, manufacturing such a device is substantially impossible. Therefore, it is difficult for a wide FSR arrayed waveguide grating requiring setting an optical path length difference extremely short, i.e., an arrayed waveguide grating having a large wavelength interval at which multiplexing/demultiplexing is performed or an arrayed waveguide grating having a number of channels to employ such a configuration.
Next, a second conventional example is described using FIG. 2. Note that PTL 1 discloses an arrayed waveguide grating filter configured as an S-shaped optical waveguide according to the second conventional example. FIG. 2 illustrates the outline of the arrayed waveguide grating optical filter according to the second embodiment. In FIG. 2, the arrayed waveguide grating optical filter is configured to include slab waveguides 1 and 2, arrayed waveguide group 3, and a sectorial arcuate waveguide group 6.
As illustrated in FIG. 2, the slab waveguides 1 and 2 are connected to each other through the S-shaped arrayed waveguide group 3, and an overall circuit configuration is substantially point symmetric. In the S-shaped optical waveguide, left arcuate waveguides 3c and right arcuate waveguides 3d are opposite in arc direction. Accordingly, in the case of directly connecting the arcuate waveguides 3c and corresponding ones of the arcuate waveguides 3d with the arcuate waveguide group 6 being omitted, respective waveguide lengths can be designed to be substantially the same. That is, the S-shaped optical waveguide is configured to once cancel out a waveguide length difference necessary in geometrical arrangement at an inflection point to zero.
In the conventional example illustrated in FIG. 2, an optical path length difference necessary for a filtering operation is given by the sectorial arcuate waveguide group 6 inserted at the inflection point of the S-shaped optical waveguide. The sectorial arcuate waveguide group 6 is configured to include arcuate waveguides among which a center point is the same, a spread angle is the same, a spacing is the same, and a radius increases by a certain amount. The optical path length difference of this circuit is determined by a waveguide length difference between any adjacent ones of the waveguides of the sectorial arcuate waveguide group 6 (a difference in radius×the spread angle), and therefore even in the case of a wide FSR, i.e., even in the case where the optical path length difference is extremely short, a desired circuit can be designed.
On the other hand, the configuration as illustrated in FIG. 2 gives rise to a problem that the waveguide is point symmetrically arranged on the basis of the S-shaped structure, and therefore the length L of the circuit is large. As a result, there is a problem that the size of the circuit exceeds the size of an effective substrate, or even in the case where the circuit can be arranged on the substrate, the number of circuits arrangeable on one substrate is small.
Next, a third conventional example is described using FIG. 3. FIG. 3 illustrates the outline of an arrayed waveguide grating optical filter according to the third conventional example. The third conventional example is the arrayed waveguide grating filter that is configured as a substantially line-symmetric waveguide group (see Patent Literature 2). As illustrated in FIG. 3, the arrayed waveguide grating optical filter includes slab waveguides 1 and 2, arrayed waveguide group 3, input waveguide 4, output waveguides 5, and sectorial arcuate waveguide group 6. In particular, the left side part of the arrayed waveguide group 3 is configured as an arrayed waveguide group 3g configured by sequentially connecting respective waveguides, i.e., linear waveguides 3a, corresponding ones of arcuate waveguides 3c, and corresponding ones of linear waveguides 3e, and the right side part of the arrayed waveguide group 3 is configured as an arrayed waveguide group 3h configured by sequentially connecting respective waveguides, i.e., linear waveguides 3f, corresponding ones of arcuate waveguides 3d, and corresponding ones of linear waveguides 3b. 
In the arrayed waveguide group 3g and arrayed waveguide group 3h, a difference in length between upper and lower ones of adjacent waveguides can be designed to be constant by, in the same manner as the design method in the first conventional example described using FIG. 1, appropriately selecting the length of each of the linear waveguides and the radius of each of the arcuate waveguides. However, protruding directions of arcs of the arcuate waveguides 3c and arcuate waveguides 3d are all upward, and therefore relative to a lower waveguide, an upper waveguide is inevitably long. That is, only the arrayed waveguide group 3g and arrayed waveguide group 3h of which the protruding directions of the arcs are the same cannot make a waveguide length difference zero.
However, in FIG. 3, protruding directions of arcs of sectorial arcuate waveguides 6 are opposite directions to those of the arcuate waveguides 3c and arcuate waveguides 3d, and therefore by appropriately selecting a spread angle and an arcuate radius of the sectorial waveguide group 6 configured to include arcuate waveguides among which a center point is the same, a spread angle is the same, a spacing is constant, and a radius increases by a certain amount, the waveguide length difference can be configured to be once cancelled out to zero. After that, by increasing or decreasing the spread angle of the sectorial waveguides by a necessary amount, the waveguide length difference of the arrayed waveguide group 3 can be easily set to a value required by a wide FSR AWG. In the case of designing an AWG by the design method according to the third example described using FIG. 3, as compared with the design method according to the second conventional example described using FIG. 2, the degree of freedom of combination of arcuate waveguides is different, and therefore an AWG having a smaller circuit size may be designable.